Broad-band dielectric spectroscopy is used to investigate the dynamics of hydration water on the surface of the cylindrical pores of a nanostructured silica material (MCM-41, with pore diameter of 3.2 nm) at various hydrations, in the temperature range 250-150 K. We focus our attention on orientational relaxations that shift from 0.5 MHz at 250 K to less than 1 Hz at 150 K. The measurements distinguish the relaxation of the hydroxyl groups at the surface of silica from the orientational dynamics of hydration water which strongly depends on the degree of hydration. Although it is significantly faster than the dynamics of water in ice, the orientational relaxation of "non-freezing" water has an activation energy comparable to that in ice when the hydration layer is complete and approximately two-molecule thick.